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Precise UAV Navigation with Cellular Carrier Phase ... · PDF file Second, cellular carrier phase measurements are modeled at a fine granularity level to consist of four terms: true

Mar 14, 2020




  • Precise UAV Navigation with Cellular

    Carrier Phase Measurements

    Joe Khalife and Zaher M. Kassas

    Department of Electrical and Computer Engineering

    University of California, Riverside

    Riverside, U.S.A.

    [email protected], [email protected]

    Abstract—This paper presents two frameworks for precise unmanned aerial vehicle (UAV) navigation with cellular carrier phase measurements. The first framework relies on a mapping UAV and a navigating UAV sharing carrier phase measurements. Experimental results show that a 63.06 cm position root mean- square error (RMSE) is achieved with this framework. The second framework leverages the relative stability of cellular base transceiver station (BTS) clocks, which alleviates the need of a mapper. It was shown through experimental data that the beat frequency stability of cellular BTSs approaches that of atomic standards and may be exploited for precise navigation with cellular carrier phase measurements. Performance bounds are derived for this framework. Experimental data demonstrate a single UAV navigating with sub-meter level accuracy for more than 5 minutes, with one experiment showing 36.61 cm position RMSE and another showing 88.58 cm position RMSE.


    Unmanned aerial vehicles (UAVs) will demand a resilient,

    accurate, and tamper-proof navigation system. Current UAV

    navigation systems will not meet these stringent demands

    as they are dependent on global navigation satellite system

    (GNSS) signals, which are jammable, spoofable, and may not

    be usable in certain environments (e.g., indoors and deep urban

    canyons) [1]–[3].

    The potential of signals of opportunity (SOPs) (e.g.,

    AM/FM radio [4], [5], iridium satellite signals [6], [7], WiFi

    [8], [9], and cellular [10]–[13]) as alternative navigation

    sources have been the subject of extensive research recently.

    Navigation with SOPs has been demonstrated on ground

    vehicles and UAVs, achieving a localization accuracy rang-

    ing from meters to tens of meters, with the latter accuracy

    corresponding to ground vehicles in deep urban canyons with

    severe multipath conditions [14]–[17].

    Cellular signals, particularly code-division multiple access

    (CDMA) and long term evolution (LTE), are among the most

    attractive SOP candidates for navigation. These signals are

    abundant, received at a much higher power than GNSS signals,

    offer a favorable horizontal geometry, and are free to use.

    Several receiver designs have been proposed recently that

    produce navigation observables from cellular CDMA and LTE

    signals [18]–[21]. Moreover, error sources pertaining to code

    phase-based navigation with cellular CDMA systems have

    This work was supported in part by the Office of Naval Research (ONR) under Grant N00014-16-1-2305.

    been derived and performance under such errors has been

    characterized [13].

    A different challenge that arises in cellular-based navigation

    is the unknown states of the cellular base transceiver stations

    (BTSs), namely their position and clock errors (bias and drift).

    This is in sharp contrast to GNSS-based navigation where

    the states of the satellites are transmitted to the receiver in

    the navigation message. To deal with this challenge, a map-

    per/navigator framework was proposed in [13], [20], where

    the mapper was assumed to have complete knowledge of its

    states (e.g., by having access to GNSS signals), estimating

    the states of BTSs in its environment, and sharing these

    estimates with a navigator that had no knowledge of its states,

    making pseudorange measurements on the same BTSs in the

    environment [13], [20]. Another framework was presented in

    which the navigator estimated its states simultaneously with

    the states of the BTSs in the environment, i.e., performed

    radio simultaneous localization and mapping (radio SLAM)

    [22]–[26]. It is worth noting that since cellular BTSs are

    spatially stationary, their positions may be mapped prior to

    navigation (e.g., by dedicated mapping receivers [27] or from

    satellite imagery and cellular databases). However, the BTSs’

    clocks errors must be continuously estimated, whether in the

    mapper/navigator framework or radio SLAM framework, since

    these errors are stochastic and dynamic.

    The relative stability of cellular CDMA BTSs clocks was

    recently studied, revealing that while these clocks are not

    perfectly synchronized to GPS, the clock biases of differ-

    ent neighboring BTSs are dominated by one common term

    [28]. Moreover, experimental data recorded over 24-hours

    showed that deviations from this common term are stable

    processes. These key findings suggest that precise carrier

    phase navigation with cellular signals is achievable with

    or without a mapper. This paper presents a comprehensive

    framework for precise UAV navigation using cellular carrier

    phase measurements. Experimental results with the proposed

    framework are presented, demonstrating sub-meter level UAV

    navigation accuracy. Another contributing factor for achieving

    such results is that cellular signals received by UAVs do not

    suffer from severe multipath by virtue of the favorable channel

    between cellular BTSs and UAVs. This can be seen in the clean

    correlation functions calculated by the receiver. These results

    are, to the authors’ knowledge, the most accurate navigation

  • results with cellular signals in the published literature. This

    paper makes three contributions, which are discussed next.

    First, two navigation frameworks for precise UAV naviga-

    tion with cellular carrier phase measurements are developed.

    The first framework consists of a mapping UAV and a navigat-

    ing UAV that utilizes carrier phase differential cellular (CD-

    cellular) measurements. The second framework consists of a

    single navigating UAV, leveraging the relative stability of the

    BTS clocks, estimating its position with a weighted nonlinear

    least-squares (WNLS) estimator.

    Second, cellular carrier phase measurements are modeled

    at a fine granularity level to consist of four terms: true range,

    common clock error, deviation from the common clock error,

    and measurement noise. The deviation term is demonstrated to

    evolve as a stable stochastic process, which is characterized via

    system identification. Moreover, experimental results over long

    periods of time validating the identified models are presented.

    The paper also discusses how to estimate the statistics of

    this process on-the-fly when the receiver has access to GNSS


    Third, the navigation performance for the second framework

    (single navigating UAV) is characterized. A theoretical lower

    bound for the logarithm of the determinant of the position

    estimation error covariance is derived and an upper bound on

    the position error is provided.

    Experimental results are provided demonstrating each of the

    proposed frameworks. Two sets of experiments are performed

    where sub-meter level UAV navigation with cellular carrier

    phase signals is achieved for periods of over five minutes.

    The remainder of the paper is organized as follows. Section

    II describes the cellular carrier phase observable. Section

    III describes the mapper/navigator framework. Section IV

    describes the single UAV navigation framework that leverages

    the relative stability of cellular SOPs. Section V derives

    stochastic models for the clock deviations and validates these

    models experimentally. Section VI establishes performance

    bounds for the second proposed framework. Section VII

    provides experimental results demonstrating each framework,

    showing sub-meter level UAV navigation accuracy. Conclud-

    ing remarks are given in Section VIII.


    In cellular systems, several known signals may be trans-

    mitted for synchronization or channel estimation purposes. In

    CDMA systems, a pilot signal consisting of a pseudorandom

    noise (PRN) sequence, known as the short code, is modulated

    by a carrier signal and broadcast by each BTS for synchro-

    nization purposes [29]. Therefore, by knowing the shortcode,

    the receiver may measure the code phase of the pilot signal

    as well as its carrier phase, hence forming a pseudorange

    measurement to each BTS transmitting the pilot signal. In

    LTE, two synchronization signals (primary synchronization

    signal (PSS) and secondary synchronization signal (SSS)) are

    broadcast by each evolved node B (eNodeB) [30]. In addition

    to the PSS and SSS, a reference signal known as the cell-

    specific reference signal (CRS) is transmitted by each eNodeB

    for channel estimation purposes [30]. The PSS, SSS, and

    CRS may be exploited to draw carrier phase and pseudorange

    measurements on neighboring eNodeBs [21], [31]. In the rest

    of this paper, availability of code phase and Doppler frequency

    measurements of cellular CDMA and LTE signals is assumed

    (e.g., from specialized navigation receivers [19] [20] [12].

    The continuous-time carrier phase observable can be ob-


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